Solve the quadratic equation by completing the square

Question

Solve by completing the square.

2x²+4x-2=0

Answer 1

Answer 2

2x^2 +4x -2 = 0

divide by 2 to simplify

x^2 +2x -1 = 0

x^2 +2x +1 = 1 +1 = 2

(x+1)^2 = 2

x+1 = +/-sqr2

x = -1 +/-sqr2= about -1+/-1.414

x = about - 2.414 or 0.414

Answer 3

Solve the following equation by completing the square:

2x ² + 4x - 2 = 0

First divide every term in the equation by 2 to get rid of the x ² coefficient. This gives us:

X ² + 2X -1 = 0

Next add 1 to both sides of the equation to move the constant over to the right side of the equation:

X ² + 2X = 1

Next divide the coefficient of X by 2, square the result, and add that result to both sides of the equation:

X ² + 2X + 1 = 2

Next divide the coefficient of X by 2 and this value is used with X to factor the left side of the equation, which by the above steps was manipulated into being a perfect square:

(X + 1)² = 2

Now take the square root of both sides of the equation in an attempt to solve for X.

√ (X +1)² = ± √ 2

This becomes:

X + 1 = ± √ 2

Finally subtract 1 from each side of the equation to get the variable X alone on one side and the constant on the other side of the equation:

X = -1 ± √ 2

This solves the quadratic equation, 2X ² + 4X - 2 = 0 for the two values of X.

Answer 4

2x²+4x-2 = 0

Divide each term by 2, you get:

x²+2x-1=0

If I add 1 to the terms x²+2x, you get a perfect square (x+1)². So, I'll add 1 to both sides of the equation

x²+2x+1-1=1

The first 3 terms represent (x+1)²

(x+1)²-1 = 1

Add one to both sides

(x+1)² = 2

Take square root on both sides

(x+1) = ±√2

 

x = -1 ± √2

These are the roots for the polynomial given

Answer 5

Answer 6

How to solve a quadratic equation by completing the square